Are irrational behaviours really irrational?

Introduction 

Are irrational behaviours really irrational? Not so much if you understand Nash's Equilibrium.

When I first read about 'Game Theory' I was hooked. It presented me with answers to the whole gamut of irrationality, the human behaviour presents. The behaviour of humans such as - why everyone in my state of Uttar Pradesh puts a water pump in their cooperative water supply to suck the maximum amount of water. If no one uses the pump then the net output is the same as when everyone uses it. In fact the optimal strategy should be that no one puts a pump and water would flow in to every house, without the extra cost of electricity needed to run the pump. Why do people still put pumps when the other solution is a cost effective one. Take another example - why do people do not choose to maintain the cleanliness or the sanctity of any collective enterprise - such as roads, railways, gardens, parks, etc? After all, we all will be better off when we collectively decide not to litter, damage or steal. I did formulate a theory around it that perhaps the 'collective' enterprises sooner or later crumble because self greed has an edge over it. Maybe this is the reason why capitalism prevails and communism is now relegated to a corner. Why didn't communism succeed? Isn't it true that if everyone works collectively towards a utopian society everyone will be better off than a few individuals who work for greed. Maybe the word 'collective' is at play here too. But when I heard about the "Game Theory", it explained all these beautifully. It now helps me to mathematically analyse a behaviour - even an emotional one - and come with a model how people would behave given a situation.

Nash' Equilibrium 

Wikipedia describes game theory as - Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers". But wait, what has Nash's Equilibrium to do with Game Theory, and what all this is about? Just play along. Ever heard of the movie - "A beautiful mind" (2001)? It is based loosely on the biography of an American mathematician - John Nash, who is one of the pioneers of the game theory. The Game Theory suggests that - people choose to behave in a given situation in such a way such that other people's decisions do not (or minimally) impact his/her outcome. This solution is called "Nash's Equilibrium". In other words - people behave in such a way that other's behaviour impacts his/her outcome, the least. Each such action - like putting a pump - littering - stealing - bribing - though unethical, actually is a Nash's Equilibrium. Though it might not be optimal but for the individual it is either the 'least risk strategy' or the 'most advantageous' one, where other people's decision doesn't make much of an impact.

Consider the case of the pump. If you put the pump and everyone does too, you get the water. If no one does but only you, then too, you get the water. So as an individual your Nash's Equilibrium is the that you put the water pump irrespective of anyone puts it or not. Let's now analyse the counter- claim. Assume that no one puts a pump and consider it to be an equilibrium. It does not require a genius to figure out that such an equilibrium would be quite an unstable one. If a few greedy people decide to switch on the pump, they will stand to gain much more than those who do not, forcing others to follow the suit. The situation would eventually gravitate towards the real Nash's equilibrium. In reality people do not have to begin with such an equilibrium state. They can start from anywhere, but soon will find themselves sucked into doing the evil what everyone else is doing. When you are with rioters, then better riot, or else..

Prerequisites 

Bribery too is an example. People who pay bribes can quickly gain ground over others who do not. Even if this behaviour is unethical it is actually the Nash's equilibrium. There enters law. Societies formulate laws to prevent such gravitation towards the equilibrium. Every country has anti-bribery laws to prevent a few people cornering most resources. They have checks and balances enforced by law to prevent the ethical decline. Sports and games have stipulated rules and are revised from time to time to nullify the effect of this equilibrium.    

A prerequisite for this mathematical analysis is that it assumes everyone is rational. People who do charity, live for others, sacrifice so that others gain on his own cost, are not counted simply because it is not a rational behaviour. In fact charity might not be a truly irrational behaviour because it stimulates your pleasure centers in your brain. That is why you might feel a high by saving someone's life at your own risk. But let's leave that part for another blog. People who citing morality, decline to use the pump but instead ask others for water, too are not counted. That water might come from someone else's pump. With this insight - go ahead and analyse yourself - do gun laws lower crime, should you displease your wife, and so on. I did not cover why people indulge in vandalism and theft of public property but I think you can figure that out on your own. Another way to counter the decline due to the equilibrium is through rewards (we covered punishments when we talked about rules and law). That is why we have examinations so that we don't fall into the Nash's Equilibrium of doing nothing. Even in an organisation too is better off rewarding the performers and punishing people for non-performance than doing nothing. Don't forget to note that this is the major difference between a private sector and a government enterprise. Usually a punishment is a more effective than a reward. That is why the law punishes citizen for being wrong but is mum on rewarding a good citizen.  

Conclusion

Game theory has many other interesting aspects. There can can be many types of games - cooperative, non-cooperative, zero sum, non-zero, iterative, etc. The possibilities are infinite. In most games there is at least one Nash's Equilibrium. In some there can be many, sometimes, infinite. But this blog is too short to cover them all. People have won Nobel prizes and have written many books on each of the topics. The one take away from this blog is to - always analyse a situation keeping the Nash's Equilibrium in mind and you will realise that people are not so irrational after all.  When you find someone who is not responding optimally to a situation, there is a good chance that he is minimising his risk (Nash's Equilibrium) or maybe he is simply insane.